In a town in which every man is clean-shaven each male either shaves himself or is shaved by the barber. The barber is a man who shaves everyone who does not shave himself (and only those who do not shave themselves). Does the barber shave himself?
To ensure that you see the paradox, think about this without reading further. The following table shows how we reach a contradiction no matter how we reason.
This is an example of the Russell Paradox, revealing that when we self-reference a set to make it a member of itself we obtain contradictions. There is no correct answer that doesn’t violate a law of logic.
